Logarithms with a Fraction as Base - Mathematics Stack Exchange
2018年1月9日 · How does one solve a logarithmic expression where the base is a fraction? In my example I am trying to solve the following: $$ n^{\log_\frac{3}{2}(1)} \tag{1} $$ This is related to using the "master theorem" to solve recurrence relations. People usually give examples where they solve something like: $$ {\log_\frac{1}{3}(27)} \tag{2} $$
Logarithm - Wikipedia
The logarithm is denoted "log b x" (pronounced as "the logarithm of x to base b", "the base-b logarithm of x", or most commonly "the log, base b, of x "). An equivalent and more succinct definition is that the function log b is the inverse function to the function x ↦ b x {\displaystyle x\mapsto b^{x}} .
对数函数 - 百度百科
如果a x =N（a>0，且a≠1），那么数x叫做以a为底N的对数，记作x=log a N，读作以a为底N的对数，其中a叫做对数的 底数 ，N叫做 真数 。 一般地，函数y=log aX （a>0，且a≠1）叫做对数函数，也就是说以幂（真数）为自变量，指数为因变量，底数为常量的函数，叫对数 ...
Logarithm Rules - ChiliMath
Learn the eight (8) log rules or laws to help you evaluate, expand, condense, and solve logarithmic equations. Try out the log rules practice problems for an even better understanding.
Logarithms - Decimals, Fractions & Tricky Cases
We learn how to calculate logarithms of decimals and fractions as well as how to deal with cases for which the input value isn't an obvious power of the base.
Logarithms - Fractional Base - Base is a Fraction
We learn the formula to calculate a logarithm whose base is a fraction. We then illustrate how to use the formula with a tutorial, in which we work through some examples as well as derive the formula. We also work through some exercises, that can even be downloaded in pdf format.
Introduction to Logarithms - Math is Fun
In its simplest form, a logarithm answers the question: How many of one number multiply together to make another number? Example: How many 2 s multiply together to make 8? Answer: 2 × 2 × 2 = 8, so we had to multiply 3 of the 2 s to get 8. We write it …
Logarithms | Brilliant Math & Science Wiki
You can rearrange any log by making a fraction, with the log of the argument in the numerator and the log of the base in the denominator. Any base can be chosen for the logs, but the bases must be the same for both logs. \(\log_2 \pi = \frac{\log \pi}{\log 2}\) \(log_a b=\frac{1}{\log_b a}\)
Laws of Logarithms or Logarithm Rules - math-for-all-grades
Express the following logarithms of fractions as difference of logarithms of numbers. log a p + log a q - log a r - log a.
Logarithms of fractions - Mathematics Stack Exchange
2019年3月18日 · Is there a convention against having a fraction passed to a logarithmic function? The reason I'm asking is for my Calculus I class. My teacher wants me to solve for x, and counts my answer as incomplete. Here's an example: My answer: x = ln (1/2) Teacher's answer: -ln (2)